Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields

Esen, İsmail; Abdelrhmaan, Alaa A.; Eltaher, Mohamed A.

doi:10.1007/s00366-021-01389-5

Cited by 44 publications

(12 citation statements)

References 90 publications

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“…Due to the softening effect on the nanoplate (Eringen 1983;Talebizadehsardari et al 2020;Esen and Özmen 2022b), the rise of the nonlocal parameter declines the frequencies inversely proportional to the size of the parameter. But the opposite results are witnessed in Fig 8, as a result of the material size parameter's stiffness-enhancing effect of the frequencies increase depending on its amount (Lim, Zhang, and Reddy 2015;Esen et al, 2021a). Here, for comparison, the amounts of nonlocal and dimensional parameters are considered the same in this study but may differ.…”

Section: Free Vibration Analysesmentioning

confidence: 79%

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Thermomechanical Response of Functionally Graded Ti-6Al-4V and Zirconia Biomaterial Plates

Özmen

2023

Journal of Materials and Mechatronics: A

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This article studies the free vibration responses of functionally graded material (FGM) porous nanoplates exposed to thermal load. The developed mathematical model includes a shear deformation, size-scale, and microstructure influence by a high-order shear deformation (HSDT) and nonlocal strain gradient (NGST) theories. The study considers four different porosity patterns across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The equation of motion of the FGM porous nanoplate, including the effects of thermal load, is derived with Hamilton's principle, and then solved analytically by employing the Navier method. For the free vibration responses of the nanoplate, the effects of nonlocal and strain gradient elasticities, temperature rise, porosity volume fraction and its distribution are analyzed.

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Section: Free Vibration Analysesmentioning

confidence: 79%

“…The effective material properties of ceramic (ZrO2) and metal (Ti-6Al-4V) material constituents can be defined as temperature-dependent with the following (Touloukian 1967;Esen, 2021a;Esen, 2021b):…”

Section: Temperature-dependent Materials Propertiesmentioning

confidence: 99%

Thermomechanical Response of Functionally Graded Ti-6Al-4V and Zirconia Biomaterial Plates

Özmen

2023

Journal of Materials and Mechatronics: A

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“…These findings may play an important role in the design of metal foam structures. Eltaher et al [ 21 ] studied the vibration and buckling behavior of FG nano beams using the nonlocal strain gradient theory. The established model can be used as a benchmark for analyzing the mechanical behavior of nano beams in a thermomagnetic field.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Size-Dependent Linear Static Bending, Buckling, and Free Vibration Based on a Modified Couple Stress Theory

Tang

Shi

et al. 2022

Materials

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The purposes of this paper are to study bending, buckling, and vibration by considering micro-scale effects using the Kirchhoff thin-plate theory and to consider small deflections, neglecting higher-order nonlinear terms. The governing equations for the bending, buckling, and vibration of the system are obtained using the equilibrium method coupled with the Kirchhoff thin-plate theory and a modified couple stress theory (MCST). The concept of the equivalent bending stiffness (EBS) of micro-thin plates is proposed to describe the scale effect. The Navier method is used to obtain analytical solutions for the bending, buckling, and free vibration of thin plates under simply supported boundary conditions with scale effects. The numerical results are presented to investigate the influence of scale effects on deflection, critical buckling load, buckling topography, and thin-plate natural frequency. The results show that the scale effect increases the equivalent stiffness of the thin plate, which leads to a decrease in deflection, a larger critical buckling load, and an increase in natural frequency, but does not affect the buckling topography. The MSCT is invalid when the thickness is greater than 10 times the scale effect parameter, thus defining the scope of application of the scale effect. This research study may contribute to the design of micro-scale devices such as MEMSs/NEMSs.

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“…Static and free vibration analyses have been executed in that paper. Furthermore, there are some important studies related to static and dynamic analyses of nanobeam structures based on nonlocal strain gradient theory [27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Transverse free vibration of nanobeams with intermediate support using nonlocal strain gradient theory

Gül¹

2022

JSEAM

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In the present study, the transverse free vibration of intermediately supported nanobeams is investigated in the framework of size-dependent nonlocal strain gradient theory. Unlike the classical elasticity theory, nonlocal strain gradient theory considers the micro/nano scale effects in mechanical analysis of size-dependent structures. The potential and kinetic energies have been derived for the nanobeam model and the Ritz method has been used to determine the natural frequencies of intermediately supported nanobeams. A cantilever nanobeam model with intermediate support is considered in the analysis. By changing the position of the intermediate support, dimensionless vibration frequencies of the nanobeam model have been obtained. Obtained results from the present nonlocal strain gradient theory showed that hardening or softening material responses have been observed according to the classical elasticity theory depending on the magnitude of the material length scale parameter and nonlocal scale parameter. This mechanical behavior can provide an advantage to designers while modeling the micro/nanostructures. Present results can be used for the design of nano-sensors, nanotube-based resonators, and oscillators.

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Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields

Cited by 44 publications

References 90 publications

Thermomechanical Response of Functionally Graded Ti-6Al-4V and Zirconia Biomaterial Plates

Thermomechanical Response of Functionally Graded Ti-6Al-4V and Zirconia Biomaterial Plates

Analysis of Size-Dependent Linear Static Bending, Buckling, and Free Vibration Based on a Modified Couple Stress Theory

Transverse free vibration of nanobeams with intermediate support using nonlocal strain gradient theory

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